Problem: Solve for $y$, $ \dfrac{1}{25y} = \dfrac{8}{25y} + \dfrac{y - 6}{15y} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $25y$ $25y$ and $15y$ The common denominator is $75y$ To get $75y$ in the denominator of the first term, multiply it by $\frac{3}{3}$ $ \dfrac{1}{25y} \times \dfrac{3}{3} = \dfrac{3}{75y} $ To get $75y$ in the denominator of the second term, multiply it by $\frac{3}{3}$ $ \dfrac{8}{25y} \times \dfrac{3}{3} = \dfrac{24}{75y} $ To get $75y$ in the denominator of the third term, multiply it by $\frac{5}{5}$ $ \dfrac{y - 6}{15y} \times \dfrac{5}{5} = \dfrac{5y - 30}{75y} $ This give us: $ \dfrac{3}{75y} = \dfrac{24}{75y} + \dfrac{5y - 30}{75y} $ If we multiply both sides of the equation by $75y$ , we get: $ 3 = 24 + 5y - 30$ $ 3 = 5y - 6$ $ 9 = 5y $ $ y = \dfrac{9}{5}$